光电子学-声光相互作用English

1、Major：电子与通信工程专业,Interaction of Light and Sound 声-光相互作用 Chapter：12.0 12.4,Outline,12.0 Introduction 12.1 Scattering of Light By Sound 12.2 Particle Picture of Bragg Diffraction Of Light By Sound 12.3 Bragg Diffraction Of Light By Acoustic WavesAnalysis 12.4 Deflection Of Light By Sound,A sound wave c

2、onsists of a sinusoidal perturbation of the density of the material , or strain, that travels at the sound velocity , as shown in Figure 12-1.,12.1 Scattering of Light By Sound,A change in the density of the medium causes a change in its index of refraction, which , to first order, is proportional t

3、o it. We can represent the sound wave shown if Figure 12-1 by (12.1-1) where . Next consider an optical beam incident on a sound wave at an angle as in Figure12-2. We can characterize the sound wave as a series of partially reflecting mirrors, separated by the sound wave-length ，that are moving at a

4、 velocity . A necessary condition for diffraction in a given direction is that all the points on a given mirror contribute in phase to the diffraction along the direction.,Considering the diffraction from two points, such as C and B in Figure 12-2, its necessary that the optical path AC-BD be some m

5、ultiple of the wavelength for diffraction along to occur. (12.1-2),The only way in which (12.1-2) can be satisfied simultaneously for all points x along a given reflector is if m=0, from which it follows that (12.1-3) In addition to the requirement that the different parts of a given acoustic phase

6、front interfere constructively, which leads to (12.1-3), we require that the diffraction from any two acoustic phase fronts add up in phase along the direction of the reflected beam. The path difference, AO+BO, of a given optical wave front resulting from reflection from two equivalent acoustic wave

7、 fronts must thus be equal to the optical wavelength . We find this condition can be written as,(12.1-4) The diffraction of light that satisfies (12.1-4) is known as Bragg diffraction.,According to the particle picture of Bragg diffraction of light by sound, a light beam with propagation vector and

8、frequency can be considered to consist of a stream of particles with momentum and energy .The diffraction of light by an approaching sound beam illustrated in Figure 12-3 can be described as a series of collisions , each of which involves an annihilation of one incident photon at and one phonon and

9、a simultaneous creation of a new photo at a frequency ,which propagates along the direction of the beam. The conservation of momentum requires that the momentum of the colliding particles be equal to the momentum of the scattered photon, so (12.2-1) The conservation of energy takes the form (12.2-2)

10、,12.2 Particle Picture Of Bragg Diffraction Of Light By Sound,If the direction of the sound beam in Figure 12-3 were reversed, the conservation-of energy principle yields The conservation-of momentum condition (12.2-1) is equivalent to the Bragg condition (12.1-4). Consider Figure 12-4. Since the so

11、und frequencies of interest are below Hz and those of the optical beams are usually above We have The magnitude of the sound wave vector is thus (12.2-3) Using , the equation becomes (12.2-4),Doppler Derivation of the Frequency Shift (12.2-2)-The formula for the Doppler Frequency Shift of a wave ref

12、lected from a moving object is From Figure 12-3 we have , thus (12.2-5) Using (12.1-4) for , we obtain (12.2-6) Therefore,We assume a long interaction path so that higher diffraction orders are missing and the only two waves coupled by the sound are the incident wave at and a diffracted wave at or ,

13、depending on the direction of the Doppler shift as discussed in section 12.2. According to 12.1 This modulation interacts with the fields at and to give rise to additional electric polarization in the medium (12.3-1) Where e(r , t) is the sum of the fields at and . The polarization will cause exchan

14、ge of power between the fields at and . We start with the wave equation modified for the case of no loss (12.3-2) Write it for the former case and assume the incident and diffracted fields are linearly polarized result in,12.3 Bragg Diffraction Of Light By Acoustic Waves-Analysis,(12.3-3) and oscill

15、ates at a frequency ,the polarization components oscillates at other frequencies are non-synchronous. The total field e(r , t) is taken as the sum of two traveling waves (12.3-4) Assuming “slow” variation of ,we combine(12.3-3) with last equation ,obtain (12.3-5) Using (12.3-1) , is given by (12.3-6

16、) Note that in taking the product ,we assume And therefore neglected non-synchronous terms with frequencies and .,Substituting (12.3-6) for in(12.3-5) leads to and similarly (12.3-7) An inspection of (12.3-7) reveals that a prerequisite for continuous cumulative interaction between the incident fiel

17、d( ) and the diffracted field( ) is that (12.3-9) Equation(12.3-9) is the Bragg condition for scattering of light by sound. Assuming that the Bragg condition(12.3-9) is satisfied, (12.3-7) becomes (12.3-10) Since, ,we took .,Defining the values of and , which correspond to a given as the respective

18、projection of along and ,we have (12.3-11) So that (12.3-10) becomes (12.3-12),Using the correspondence between , and , we have (12.3-13) It is of sufficient generality to describe the interaction between two input fields at and with arbitrary phase, and arbitrary amplitudes as long as the Bragg con

19、dition and the frequency condition are fulfilled. In the special case of a single frequency input at , (12.3-14) (12.3-15) So that the total optical power carried by both waves is conserved.,If the interaction distance between the two beams is such that ,the total power of the incident beam is transferred into diffracted beam. The fraction of the power of the incident beam transferred in a distance into the diffracted beam is given, using(12.3-8) and (12.3-14) by (12.3-16) Using strain and ,we obtain (12